Welfare costs of business cycles when markets are incomplete

This paper analyzes the welfare costs of business cycles when workers face uninsurable idiosyncratic labor income risk. In accordance with the previous literature, this paper decomposes labor income risk into an aggregate and an idiosyncratic component, but in contrast to the previous literature, this paper allows for multiple sources of idiosyncratic labor income risk. Using the multi-dimensional approach to idiosyncratic risk, this paper provides a general characterization of the welfare cost of business cycles when preferences and the (marginal) process of individual labor income in the economy with business cycles are given. The general analysis shows that the introduction of multiple sources of idiosyncratic risk never decreases the welfare cost of business cycles, and strictly increases it if there are cyclical fluctuations across the different sources of risk. Finally, this paper also provides a quantitative analysis of multi-dimensional labor income risk based on a version of the model that is calibrated to match U.S. labor market data. The quantitative analysis suggests that realistic variations across two particular dimensions of idiosyncratic labor income risk increase the welfare cost of business cycles by a substantial amount.